New York has won two straight after a season-opening loss. Tampa Bay has lost three of its first four games this year, all of which have come on the road.
Tavares opened the scoring 36 seconds into the contest and then put a slap shot past Dwayne Roloson with 4:45 to go in the first period to make it 3-1.
The only Tampa Bay goal came from Steven Stamkos. It was his first of the season after producing 96 over the past two years.
Al Montoya stopped 34-of-35 shots for the Islanders.
Roloson gave up all five goals on 18 shots before being removed in favor of Mathieu Garon, who made 16 saves.